We report on the experimental estimation of a lower bound of helium. Our experiment differs from a previous one described by Hasegawa et al. [Phys. Rev. A 71, 023407 (2005)]. The photons that correspond to the 27th harmonic of a Ti:sapphire laser have an energy of 41.8 eV. The extraction of the cross section rests on a theoretical model, based on the rate equations, that fully includes the contribution from the sequential channels and the macroscopic effects. Some of the experimental parameters are very difficult to measure accurately. For those parameters., we deliberately consider values compatible with their experimental determinations and that lead systematically to an underestimation of the two-photon double ionization cross section. Our estimation of this lower bound is higher than a bunch of various theoretical results. It stays, however, too close to these latter ones to draw any definite conclusion about their validity, even though it clearly indicates that the actual value of the double ionization cross section is higher than expected.